🧮 algebra

1. **State the problem:** Simplify the expression $$(x^2 - 4y)^2 - (x^2 + 4y)^2$$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule $$a

1. **State the problem:** Explain why the equation uses $2g$ instead of just $g$ when solving for the number of girls. 2. **Recall the equation:** The total number of boys and girl

1. **State the problem:** There are 35 more boys than girls in a village, and the total number of boys and girls is 137. We need to find how many boys are there. 2. **Define variab

1. **State the problem:** Solve for all values of $c$ such that $5 = \left| \frac{c}{3} \right|$. 2. **Recall the definition of absolute value:** For any real number $x$, $|x| = a$

1. The problem is to solve the equation $$|6x| = 36$$ for all values of $x$. 2. Recall that the absolute value equation $|A| = B$ means $A = B$ or $A = -B$ when $B \geq 0$.

1. **Problem:** Show that $x + a + y$ is a factor of the determinant $$\begin{vmatrix} a & x & y \\ x & a & y \\ x & y & a \end{vmatrix}$$

1. **Problem 1: Find the determinant of matrix A** Given matrix $$A=\begin{bmatrix}2 & 3 & 5 \\ 4 & 1 & 6 \\ 1 & 4 & 0\end{bmatrix}$$

1. **Planteamiento del problema:** Queremos maximizar el ingreso económico $I(d)$ de una empresa de telefonía celular que ofrece disminuciones en la cuota mensual para captar nuevo

Let's look at your problem: $\frac{5x}{5x}$. 1️⃣ Imagine you have 5 apples 🍎 🍎 🍎 🍎 🍎 and you put them into 5 groups of x apples each.

Let's solve $x + x$ step by step! 🎉 **Step 1:** Imagine you have <span style='font-size: 2em;'>🍎</span> one apple.

1. **State the problem:** Simplify the expression $a + a \times a$. 2. **Recall the order of operations:** Multiplication is performed before addition.

1. **State the problem:** We need to graph the rational function $$R(x) = \frac{x + 6}{x(x + 12)}$$. 2. **Identify intercepts:**

1. **State the problem:** We need to analyze the rational function $$R(x) = \frac{x+6}{x(x+12)}$$ to determine where its graph is above or below the x-axis and identify the correct

1. **Problem statement:** A student answered 120 True/False questions. Each correct answer gives 1 mark, each wrong answer deducts 1/4 mark. The student scored 90 marks. If all gue

1. The problem is to calculate the final grade based on weighted components. 2. The weights and achieved percentages are:

1. **State the problem:** Solve for $w$ in the equation $1.74 = w - 3.68$. 2. **Formula and rule:** To isolate $w$, add $3.68$ to both sides of the equation to cancel out the $-3.6

1. **State the problem:** Evaluate the expression $\frac{x}{6} + 3$ when $x = -24$. 2. **Substitute the value:** Replace $x$ with $-24$ in the expression:

1. **State the problem:** Calculate the product of the mixed fractions $1 \frac{7}{8}$ and $2 \frac{7}{15}$ and express the result as a reduced mixed fraction. 2. **Convert mixed f

1. The problem is to find the number of terms in the finite arithmetic sequence: 16, 11, 6, 1, ..., -239. 2. The formula for the $n$-th term of an arithmetic sequence is:

1. **State the problem:** Calculate the product of the fractions $\frac{6}{7} \times \frac{14}{21} \times \frac{14}{3}$.\n\n2. **Recall the multiplication rule for fractions:** Whe

1. **Problem:** The function $y=5\sin(x)-7$ is translated to $y=5\sin(x)$. We need to find the translation. 2. **Understanding the problem:** The original function is shifted verti